For me, the most succinct and illuminating portrait of the Doors is still Joan Didion's masterful account of the evening she spent in the spring of 1968 "sitting on the cold vinyl floor of a sound studio on Sunset Boulevard" waiting for their lead singer, Jim Morrison, to turn up for a recording session. Stretching over just five pages, it was one of several sharp vignettes of countercultural life in California that made up the title essay of her second book of nonfiction, The White Album, published in 1979.

A detached but astute observer of the excesses of the late 1960s, Didion saw the Doors as a kind of dark Dionysian counterpoint to the utopian dreams of the time. "On the whole my attention was only minimally engaged by the preoccupations of rock-and-roll bands," she wrote, "but the Doors were different, the Doors interested me. The Doors seemed unconvinced that love was brotherhood and the Kama Sutra. The Doors' music insisted that love was sex and sex was death and therein lay salvation." She dubbed them "the Norman Mailers of the top 40, missionaries of apocalyptic sex".

Greil Marcus does not do succinct or detached. He is passionate, scholarly and deadly serious, sometimes to the point of unconscious self-parody, about the music he loves, whether it be the young Van Morrison or an obscure punk group such as the Mekons. In some ways, this makes him the perfect writer to take on board the Doors's contested legacy.

Some 40 years on from their short reign as Los Angeles's most portentous rock group, the Doors are still revered by some for the dark power of their lyrics and swirling music, and dismissed by others as pompous and overblown. The premature death of their lead singer and self-styled poet, Jim Morrison, in Paris in 1971, ensured the group's place in rock mythology, though Oliver Stone's 1991 biopic, which Marcus reappraises in a positive light here, may have dented that mythology for younger rock fans unused to such displays of emotional melodrama, on and offstage.

This book, though, is not so much a defence of the Doors as a celebration of what the group – and, by extension the 60s – represented. In one of the most thought-provoking chapters, titled "The Doors in the So-Called Sixties", Marcus writes: "The Sixties are most generously described as a time when people took part – when they stepped out of themselves and acted in public, as people who didn't know what would happen next, but who were sure that acts of true risk and fear would produce something different from what they had been raised to take for granted."

I would have loved a whole book on this subject, but Marcus, as ever, has a lot of ground to cover. That his scholarship often gives way to wild extrapolation is a Marcusian signature of sorts, and one that will irritate as many readers as it intrigues. The chapter devoted to the song "Twentieth Century Fox", for instance, reads as if he is musing aloud, leaping from a brief explanation of the lyric to the ways in which the song resembles a piece of pop art by Eduardo Paolozzi and a piece of classic pop music by Chuck Berry. This leads to a meditation on the difference between high and low pop art – Roy Lichtenstein v George Herriman, the creator of Krazy Kat – followed by an interrogation of Richard Hamilton's pop aesthetic. Before you've caught your breath, Marcus has moved on to a description of the underrated Wallace Berman's serial photographic assemblages and the graphic power of the flyers designed by Shawn Kerri for punk band the Germs.

All this is classic Marcus territory and it makes dizzying reading, but to what end? Were the Doors making pop art of a kind or not? Or, only briefly? And what to make of this assertion: "If 'Light My Fire' hadn't made the Doors into stars you can hear how their music could have curdled into artiness, everything self-referential, postmodern, each not a parody of something else, not a word having to mean what it said, the group more popular in Paris or Milan, especially during fashion week, than anywhere in America, just like Chet Baker." Phew! An interesting point that might have been better made without the whiff of cultural imperialism and rock snobbery. And when he writes of Jim Morrison being "engaged in a race against language for its own sake", you may, like me, feel he is unconsciously describing his own writing style.

When Marcus gets it right, though, he is an exhilaratingly original critic, taking the reader on a journey way beyond the tired cliches of most rock writing. His first book, Mystery Train, which places rock music in the context of American myth and folklore, is a case in point. So, too, is the constantly illuminating Invisible Republic, in which he explored "the old weird America" that Bob Dylan mined on The Basement Tapes. This time around, his treatise seems less assured, or perhaps less developed. There is no guiding theme to the book save for the one suggested in the subtitle: "A Lifetime of Listening to Five Mean Years". The song-by-song approach works to a degree, though many of the versions he refers to are rare recordings or live bootlegs which only the true devotee will be prepared to track down.

Few bands epitomise the contradictions of the 60s like the Doors, whose music contained all the promise and the possibility of that time, as well as the chaos and the disorder. On a good night, they could sound like the best bar band in the world (the rough and tumble of "Roadhouse Blues", the surging momentum of "LA Woman") and be psychic explorers in tune with Vietnam-era America's collective death wish (the spiralling 12-minute Freudian saga that is "The End", later used brilliantly by Francis Ford Coppola to open Apocalypse Now, a movie that portrays Vietnam as the ultimate bad acid trip).

Marcus's spiralling mediation did send me back to the band's music for the first time in ages, and I was arrested once again by the lyrical and musical spell of songs such as "Soul Kitchen" – "Your fingers weave quick minarets/ Speak in secret alphabets/ I light another cigarette/ Learn to forget…" Marcus describes "Soul Kitchen" as "the Doors' own 'Gloria'", though there is nothing in the Van Morrison song as beautifully defeated as that "learn to forget" line.

This book may well make the most sceptical music fan think again about the Doors and their music, as well as the times that shaped them and they, in turn, helped shape. The reader will need a certain stamina and patience, but, as usual with Marcus, it's worth it in the end.